topological insulators & their spintronics application xue-sen wang national university of...
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Topological Insulators &
Their Spintronics Application
Xue-sen WangNational University of Singapore
Topological Insulator: A piece of material that is an
insulator (or semiconductor) in its bulk, but supports
spin-dependent conductive states at the boundaries
due to spin-orbital coupling
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Spintronics in Future Information Technology
(S-Q Shen, AAPPS Bulletin 18(5), 29)
Spintronics: Manipulation of electron spin for information
storage, transmission & processing
Traditional spintronics: e.g. magnetic disk, size limit
Current spintronics: e.g. GMR, TMR, still with a charge
current
Ideal Spintronics: Pure spin current & spin accumulation
controlled by electric field/voltage, dissipationless
Quantum spin Hall effect (QSHE): an attractive option
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Hall Effect & Spin Hall Effect (SHE)
(From Y.K. Kato, Sci. Am. 2007(10) 88; also see Hirsch, PRL 83, 1834)
SHE: Separate electrons of different spins without using a magnetic field
Spin current can be generated & controlled
with an electric field or voltage, important to spintronics
)(2 jjjS e
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Observations of Spin Hall Effect
SHE
Reverse SHE
(Valenzuela & Tinkham, Nature 442, 176; Kent, Nature 442, 143)
Electronic measurement:
A spin Hall voltage VSH
generated by Reverse-SHE
Spin accumulation at
edges of GaAs stripe
observed by Kerr rotation
microscopy
(Kato et al., Science 306, 1910)
E
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Mechanism of SHE: Spin-dependent scattering
Extrinsic mechanism: Scattering by magnetic field or
magnetic impurities
Zeeman energy: BμU
Stern-Gerlach effect: BμF )(
From relativity, an electron
moving in an electric field feels a magnetic field
Intrinsic mechanism:
EβB ceff
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sp )( VH RR Intrinsic Rashba spin-orbit coupling:
R: small in light atoms (< 1 meV), significantly enhanced in
narrow-gap semiconductors containing Bi, Hg…
More observable in low-D structures, controllable with electric field
A moving electric field induces a magnetic field:
V: potential gradient in atom, or at a boundary:
1) Edges of a 2D electron gas
2) Surface or Interface, adjustable with bias voltage
Rashba Effect EβB ceff
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Boundary states & SHE sp )( VH RR
A stripe of 2DEG
0V 0V
Non-zero and opposite V at two edges (or surfaces) of a 2DEG
channel (or a film) Spin-filtered edge (surface) states
A thin film
V = 0 in bulk region if it has inversion symmetry
Major contribution to V still comes from atomic potential
Edge
Surface
×
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Spin-Orbital Coupling in 2DEG or on Surface
(Sinova et al., PRL 92, 126603; Ast et al., PRL 98, 186807)
sp )( VH RR
ARPES of Bi/Ag(111)
σek z// )(RRH or:
k
s
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Quantized conductance through a quantum wire or point contact:
Transmitted states (modes) Ntrans, can be changed by gate bias Vg
trans0trans
22 NGNheG
Quantum conductance unit: G0 = 2e2/h = 7.75 S
Quantum Transport in Low-D Systems
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Edge states & QHE in 2DEG Channel
Skipping OrbitsTo
Edge States
2DEG in a normal B
Four-terminal Hall resistance:
neh
IVV
IVV
R 12
24
13
2424,13
or: hne
xy
2
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Quantum Hall Effect & Quantum Spin Hall Effect in 2D
(Nagaosa, Science 318, 758; Day, Phys. Today 61(1), 19; Kane & Mele, PRL 95, 146802)
E
kValence band
Conduction band
Bulk Insulator with Spin-dependent Kramers-pair gapless edge states
Kramers-pair Edge States: elastic backscattering forbidden by
time reversal symmetry, robust against weak disorder
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Graphite
1.42 Å
K
M
Γ
K’ Dirac point
Mass-less (relativistic) fermion
Zero bandgap
Semimetal
Single-layer graphite:
Graphene
3.4 Å vkE
DOS |E|
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QSHE in Graphene
(from Kane & Mele, PRL 95, 226801)
Spin-orbit coupling for edge
states: sp )( VVSO
x
y
Spin-filtered edge states: Electrons with
opposite spin propagate in opposite
direction; jS may be non-dissipative
A spin current will flow between leads
attached to the opposite edges:
2/eVI S
Quantized SH conductivity: 2/esxy
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Graphene: a 2D Spin Hall insulator
Generate a spin current without dissipation
Spin-filtered edge states in graphene are insensitive to disorder:
Elastic backscattering is prohibited by time reversal
Existence of other spin Hall insulators with stronger SO interaction?
Spin Hall gap in graphene: 2SO ~ 2.4 K
(Kane & Mele, PRL 95, 226801; only ~ 0.01 K in Yao et al, PRB 75, 041401)
Operation temperature not practical!
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More attractive materials for Spintronics
Bi, Z = 83; Pb, Z = 82; Hg, Z = 80; strong SOC
Semimetal or narrow-gap semiconductor
Bulk carrier density ~1017 cm-3, low bulk conductivity
Surface carrier density ~1013 cm-2, surface conduction
may be dominant
Small effective mass: m* = 0.002m0, ~ 106 cm2/Vs,
Fermi velocity vF 106 m/s (comparable with
graphene)
2D & 3D Topological insulators possible
HgTe QW, Bi, Bi1-xSbx , Bi2Se3
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Inverted Normal
(König et al., Science 318 (2007) 766)
QSH Edge States in HgTe QW
Critical QW thickness 6.3 nm
5.5 nm
7.3 nm
Inverted?
Normal Normal
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Lattice Structure of Bi
Rhombohedral lattice
A
B
C
]112[_
]101[_
4.545 Å
3.95 Å
abc
= 57.23˚
Covalent bond
Honeycomb bilayer
Stacking in [111] direction
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Bi(111) bilayer: a 2D Spin Hall Insulator
abc
Covalent bond
Honeycomb bilayer
}
[111]
]112[_
]101[_
(Murakami, PRL 97, 236805; Liu et al., PRB 76, 121301)
2D bandgap 0.2 eV
1 Kramers pair of edge states
Spin Hall Conductivity:
474.0~ es
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(Koroteev et al., PRL 93, 046403; Liu et al., PRB 76, 121301)
SOC of Bi(111) surface states
Splitting ~ 0.1-0.2 eV
Spin accumulation at edges of Bi(111) bilayer
With SOC
Sz +
Sz -
When EF in middle of Eg
No charge current
MΓ
K
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Number of Kramers pairs at each edge/surface must be odd
(non-zero Z2 invariant): Strong Topological Insulator
E
kValence band
Conduction band
Quantum spin Hall Effect in 3D
Kramers pair
2D Edge states
3D Surface states
(Kane & Mele, PRL 95, 146802; Fu & Kane, PRB 76, 045302)
(Weak topological insulator: with even number of edge-state pairs)
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(S-c Zhang, APS Physics 1, 6 (2008))
Strong Topological Insulator
Metallic edge/surface states linear in k meet at an
odd number of points in k-space
Robust against perturbation
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Lattice Structure of Sb & Bi
Rhombohedral lattice:
A distorted simple cubic (SC) or FCC
lattice
A
B
C
]112[_
]101[_
Sb: 4.31 Å
Bi: 4.545 Å
Sb: 3.76 Å
Bi: 3.95 Å
abc
= 57.1 (Sb) = 57.23° (Bi)
Covalent bond
Honeycomb bilayer
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Electronic Structure of Bi & Sb
EF= 26.7 meV
L
13.8 meV
Band overlap 38 meV
Low carrier density (~1017 cm-3)
Small effective mass
High carrier mobility (~ 105 cm2/Vs)
Long F, ~ 120 Å
T
(for Sb: at H, 177 meV
overlap with inverted La)
La
Ls
Semimetal
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Energy Bands of Bi1-xSbx
@ x ~ 4%: Dirac Fermions in 3+1 D
kvkvk 22)()(E
TE
x (%)T
H
H
0 4 7 9 17 22
La
LaLa
Ls
LsLs
30 m
eV
Semiconductor or
Topological Insulator
Inversion of L bands
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(Hsieh et al., Nature 452, 970; Teo et al., PRB 78, 045426)
Bi1-xSbx: Topological Insulator
m* ~ 0.002me
(x ~ 7-10%)
3D quantum spin Hall phase 2D surface states
2D quantum spin Hall phase 1D edge states
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(Hsieh et al., Nature 452, 970 (Suppl. Info.))
Effect of SOC on Bi
bulk band near EF
= 13.7 meV
3D Dirac point at L
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(from Teo, Fu & Kane, PRB 78, 045426)
Surface States on Different Bi1-xSbx Surfaces
Surface time-reversal-invariant momentum (TRIM)
enclosed by an odd number of electron or hole pockets
Surface Fermi arc
encloses 1 or 3 Dirac
points on all surfaces
“Strong” Topological Insulator
(111) & (110) surfaces
commonly observable
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Bi(111) Surface
(Hofmann, Prog. Surf. Sci. 81, 191; Ast & Hochst, PRL 87, 177602)
ARPES measurement of surface states
EF mapping K
Spin direction
of states at EF
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Bi(110) Surfaces
1X
2X
ARPES & computed of surface states
EF mapping &
spin directions
(Hofmann, Prog. Surf. Sci. 81, 191; Pascual et al., PRL 93, 196802)
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HOPG or MoS2
cleaved in air, ~ 5
hours degas at 300-
550C in UHV
Sb & Bi from thermal
evaporators
Nearly free-standing
structures grow on
aninert surface
STM imaging at RT
UHV STM system
Bi & Sb Nanostructures Grown on Inert Substrates
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3D, 2D & 1D Sb Nanostructures on HOPG
Sb4, F = 4 Å/min, 12 Å
deposited at RT. 3D, 2D & 1D islands formed at early stage
(1000 nm)2
1D, h ~ 23 nm
3D, h ~ 60 nm
2D, h ~ 3.5 nm
(100 nm)2
(10 nm)2
(111)-oriented 2D islands
Lateral period:
a = 4.170.12 Å
Bulk Sb: a = 4.31 Å
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1D & 2D Bi Nanostructures on HOPG
(1 m)2
2D islands, height ~ 1 nm
(111) oriented
(0.6 m)2
1D nanobelts
Bi(111) bilayer spacing: 3.95 Å
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Bi Nanobelts: (110) oriented
Belt surface with rectangular lattice:
4.34 Å × 4.67 Å
(200 nm)2
(2 m)2
Height ~ 1-10 nm
Width ~ 25-70 nm
Narrow belts on
top of wide belt
(9 nm)2
Narrow belt
h ~ 8 Å
Bulk Bi(110): 4.55 Å × 4.75 Å
Layer spacing: 3.28 Å
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Bi(110) nanobelts on Bi/Ag(111)
Aligned Bi Nanobelt on Low-symmetry Surface
Aligned Bi nanobelts on Si(111)-
41:In single-domain terrace
observed in Surface Physics Lab,
Inst. of Physics, CAS, Beijing
Bi wetting layer on
Ag(111): with a 2D
rectangular lattice
(300 nm)2
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Dangling bondsInert sidewall
Deposited atoms
Self-Assembly of Sb & Bi Nanobelts
(111) top surface of Bi nanobelt
Growth direction
Removal of dangling bonds on Bi(110) by “puckered-layer” atomic reconfiguration (Nagao et al. PRL 2004)
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Transformation of Bi(110) to Bi(111)
(1 m)2
(1 m)2
After 10 min 100C annealh ~ 5 – 9 nm
After 10 min 130C annealh ~ 5 – 10 nm
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(H. Zhang et al., Nature Physics 5 (2009) 438)
Topological Insulators at
Room Temperature
Bi2Se3: Eg 0.3 eV
Surface states on (111)
Sb2Te3: Eg 0.1 eV
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Magneto-Electric Effects in Topological Insulators
Normal insulator:
223
0
1BE
xdtdS
Additional action term: BExdtdS 3
22
137/1/2 ce where
AAxdtd 3
42
Topological insulator: θ = πNormal insulator: θ = 0;
All time reversal invariant insulators can be divided into two classes:
(Qi, Hughes and Zhang, PRB 78, 195424)
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Topological Magneto-Electric (TME) Effect
P3 = θ/2π
(Qi, Hughes and Zhang, PRB 78, 195424; Qi et al, arXiv:0811.1303)
A charge near TI induces an
image magnetic monopole:
g qP
g 32
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Summary
Topological insulators possess novel properties with potential
spintronic applications due to QSHE
HgTe QW, Bi(111) monolayer, Bi1-xSbx alloy, Bi2Se3 and Sb2Te3 are
possible topological insulators
Bi(111) bilayer/film similar to graphene/graphite
Ultrathin (2-6 bilayers) Bi(111) and Bi(110) nanobelts can be
obtained on inert substrates (e.g. graphite and MoS2)
Bi & Sb nanostructures can be fabricated at much less demanding
conditions than for graphene. Certain growth controls have been
accomplished
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Further Studies
Fabrication of Bi1-xSbx (x ~ 10%) thin films and
nanostructures, effect of inhomogeneity
Electronic & spintronic transport measurements, TME
effect: contact, patterning and processing
Controlled growth of Bi & BiSb structures on Si-based
substrates
Other topological materials, e.g. Bi2Se3, Sb2Te3
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Universal Intrinsic Spin Hall Effect in 2DEG
(Sinova et al., PRL 92, 126603)
xE x ˆys ,j
Spin current is
polarized in z direction,
with spin Hall conductivity
ys ,j
8, e
E
jσ
x
yssH
Still need charge current xc,j
p
s
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(Raghu et al., PRL 100, 156401)
U
V1
V2
Phases of Honeycomb Lattice with Repulsive Interactions
QSE phase more likely in bilayer
lattice of dipolar atoms with
V2 > U, V1
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D
A
C
B
y
x
A: ax = 4.47 Å
Lattice distortion across 90-elbow of Bi nanobelt
B: ax = 4.49 Å
C: ax = 4.73 Å
D: ax = 4.88 Å
Variation of X-period
Reverse variation of Y-period
On bulk Bi(110): 4.55 Å × 4.75 Å
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2 bilayer (~ 6.6 Å) Bi(110) growth
On Ag(111) with a Bi wetting layer
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Semimetal-to-Semiconductor transition in Bi nanowires
(Lin et al., PRB 62, 4610)
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Bi(111) Ultrathin Films
electron
hole
1 bilayer: Semiconducting
With SOC
2 – 3 bilayer films: Semimetallic
(Koroteev et al., PRB 77, 045428)
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Bi(110): bilayer pairing
Remove dangling bonds on Bi(011) by
“puckered-layer” pairing reconfiguration
(Nagao et al. PRL 2004) >10% in vacuum
(Koroteev et al., PRB 77, 045428)